An aeroplane was flying horizontally with a velocity of 720 km / h at an altitude of 490 m . When it is just vertically above the target a bomb is dropped from it. How far horizontally it missed the t

Question

An aeroplane was flying horizontally with a velocity of 720 km / h at an altitude of 490 m . When it is just vertically above the target a bomb is dropped from it. How far horizontally it missed the target?

TestHub · Accepted Answer

To find the horizontal distance the bomb travels, we first calculate the time it takes to fall from 490 m.

Given:

Initial horizontal velocity, $u_{x} = 720 km / h = 200 m / s$

Altitude, $h = 490 m$

Acceleration due to gravity, $g = 9.8 m / s^{2}$

For vertical motion:

$h = u_{y} t + \frac{1}{2} g t^{2}$

Since the bomb is dropped, $u_{y} = 0$ .

$490 = 0 \cdot t + \frac{1}{2} (9.8) t^{2}$

$490 = 4.9 t^{2}$

$t^{2} = \frac{490}{4.9} = 100$

$t = 10 s$

For horizontal motion:

The horizontal velocity remains constant.

Horizontal distance, $x = u_{x} t$

$x = 200 m / s \times 10 s$

$x = 2000 m$

The bomb travels 2000 m horizontally, so it misses the target by 2000 m.

The final answer is $2000 m$ .

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